Dimensional Space Research Articles

Supersymmetric spectrum for vector multiplet on Euclidean AdS2

Quantum study of supersymmetric theories on Euclidean two dimensional anti-de Sitter space (EAdS2) requires complexified spectrum. For a chiral multiplet, we showed that the spectrum of the Dirac operator acquires a universal shift of i/2 from the real spectrum to make the supersymmetry between boson and fermion manifest, where both the bosonic and fermionic eigenfunctions are normalizable using an appropriate definition of Euclidean inner product. We extend this analysis to the vector multiplet, where we show that the gaugino requires both +i/2 and i/2 shift from the real spectrum, and there is additional isolated point at vanishing spectral parameter which is mapped by supersymmetry to the boundary zero modes of the vector field. Furthermore, this spectral analysis shows that not every bosonic fields in the vector multiplet can satisfy normalizable boundary condition. Nevertheless, aided by a reorganization of fields into a cohomological form, we find the supersymmetry mapping between bosons and fermions in terms of the expansion coefficients with respect to the newly constructed basis.

EEG classification of resting state and arithmetic cognitive workload using functional connectivity of different frequency bands and machine learning techniques

ABSTRACT This study aimed to perform a comparative study of the functional connectivity of different frequency bands for the identification of resting and arithmetic cognitive workload EEG using machine learning techniques. Functional connectivity was calculated from preprocessed EEGs for both rest and task states in 5 EEG sub-bands: alpha (8–13 Hz), theta (4–8 Hz), delta (1–4 Hz), gamma (30–45 Hz), and beta (13–30 Hz). This was done through Weighted Phase Lag Index (WPLI). After that, PCA was applied to the calculated feature vectors to decrease the dimensionality of the feature space. Eventually, the normalized chosen features were used as input for different machine learning-based classification models, and the performance was assessed through the leave-one-subject cross-validation (LOSOCV) algorithm. Experimental results showed that the classification results on the basis of the connectivity features of delta, theta, alpha, beta, and gamma frequency bands were 90.27%, 77.78%, 62.50%, 62.50%, and 76.39%, respectively. The obtained results showed that used machine learning models and functional connectivity technique are successfully applied to detect mental workload from rest- and task-EEG. In summary, EEG functional connectivity in the delta frequency is a potent tool for comprehending the neural basis of mental workload and has significant applications in various fields.

Three-Dimensional Evaluation of Condylar Position and Joint Spaces Following Orthodontic Treatment With Quadruple Premolar Extractions.

This study aimed to assess the alterations in the temporomandibular joint among adult patients undergoing orthodontic treatment involving the extraction of four premolars. A cohort of 44 adults, with a mean age of 24.2 years, underwent orthodontic therapy that included quadruple premolar extractions. Cone-beam computed tomography scans were performed before and after the treatment to evaluate the temporomandibular joints. The three-dimensional assessment focused on the condylar position relative to the cranial base and the articular fossa, the axial condylar rotation, and the joint spaces. Notably, a significant posterior shift of the condyle was detected (P≤0.01), averaging a 0.41mm retraction. The posterior joint space narrowed by 0.32mm post-treatment. Additionally, a medial tilt of 0.62° in the condyle's long axis was observed in the frontal plane. No significant changes were recorded for the other condylar positions, rotations, or joint space dimensions. The findings suggest that orthodontic treatment with four premolar extractions may instigate condylar repositioning and rotation. These insights can inform refinements in treatment protocols.

Nonlinear seismic response analysis of liquefiable sites based on effective stress method

In this study, the one-dimensional nonlinear Matasovic model was extended to the two- and three- dimensional stress space by replacing the shear strain with the generalized shear strain. The extended Matasovic model was subsequently combined with Dobry’s excess pore water pressure generation model, and the reliability of the proposed loosely coupled effective stress analysis model was verified through undrained cyclic triaxial tests and a one-dimensional site response analysis. Finally, this method was applied to an engineering site in China to evaluate the nonlinear seismic response of liquefiable sites. The results show that the proposed effective stress analysis method can capture the dynamic behavior of the soil and the generation of pore water pressure during strong shaking. Moreover, there are differences between the proposed effective stress analysis method and the total stress analysis method for liquefiable sites, which indicates the need for careful selection in practical applications.

General Relations between Stress Fluctuations and Viscoelasticity in Amorphous Polymer and Glass-Forming Systems.

Mechanical stress governs the dynamics of viscoelastic polymer systems and supercooled glass-forming fluids. It was recently established that liquids with long terminal relaxation times are characterized by transiently frozen stress fields, which, moreover, exhibit long-range correlations contributing to the dynamically heterogeneous nature of such systems. Recent studies show that stress correlations and relaxation elastic moduli are intimately related in isotropic viscoelastic systems. However, the origin of these relations (involving spatially resolved material relaxation functions) is non-trivial: some relations are based on the fluctuation-dissipation theorem (FDT), while others involve approximations. Generalizing our recent results on 2D systems, we here rigorously derive three exact FDT relations (already established in our recent investigations and, partially, in classical studies) between spatio-temporal stress correlations and generalized relaxation moduli, and a couple of new exact relations. We also derive several new approximate relations valid in the hydrodynamic regime, taking into account the effects of thermal conductivity and composition fluctuations for arbitrary space dimension. One approximate relation was heuristically obtained in our previous studies and verified using our extended simulation data on two-dimensional (2D) glass-forming systems. As a result, we provide the means to obtain, in any spatial dimension, all stress-correlation functions in terms of relaxation moduli and vice versa. The new approximate relations are tested using simulation data on 2D systems of polydisperse Lennard-Jones particles.

Accommodating beginner language learners in level-based language introduction

The paper builds on ethnographic fieldwork in a Language Introduction program for recently arrived students in an upper secondary school in Sweden. In a short period of time, this program prepares students for using Swedish as an academic language, in order to enter a national program. One response to this challenge is that schools allocate the recently arrived students to level-based groups. We contribute new knowledge about this practice by focusing on the nature of teacher support in one beginner group and one more advanced group, based on ethnographic data from classroom observations and interviews. Drawing from language scaffolding theory, we show how the teachers in both groups initiated collaborative dialogue. This dialogue was most prominent in peer work in the advanced group, affording space for flexible language use and affective-relational dimensions. The peer work seemingly compensated for less teacher bridging to students’ previous language resources, less explicit feedback, and less use of multimodality. The findings contribute new knowledge about how teachers accommodate beginner learners in their everyday teaching, although accommodating all students was not feasible. Other possible ways of grouping and supporting learners while closely attending to learner development could be explored further.

The study on the coupled influence of water saturation on heat and mass transfer processes within porous media under CW laser irradiation

Continuous wave (CW) laser irradiation induces temperature changes in various phases within porous media, accompanied by phase change and gas transport. Water saturation is a crucial factor influencing this context's moisture and heat transfer process. This paper addresses this issue by establishing a theoretical model for CW laser irradiation on unsaturated porous media. Through experiments and simulations, it studies the effects of different water saturations on heat and mass transfer under laser irradiation. The results indicate that the critical depth reflects the influence of water saturation under laser irradiation on the distribution of solid-phase temperature in both time and space dimensions. Specifically, an increase in water saturation enhances the uniformity of solid-phase temperature distribution, while the gas temperature exhibits a similar distribution pattern. For mass transfer processes, it increases the evaporation rate and Darcy velocity of porous media within the effective range of laser irradiation. Lower water saturation facilitates phase change processes and accelerates gas transport rates. Importantly, this trend remains consistent even with the emergence of dry-saturation zones. Additionally, the decrease in water saturation has a coupled promoting effect on gas temperature and mass transfer processes. Lowering water saturation can increase gas temperature and consequently enhance mass transfer processes. Simultaneously, enhancing mass transfer processes benefits heat exchange between the two phases. In the four sets of experiments, the conformity of the surface temperature rise curves obtained from experiments and simulations is good, indicating that the model can accurately reflect the temperature rise patterns of sand particles. In summary, this work provides valuable research results on the effects of different water saturations on laser irradiation-induced temperature rise, phase change, and gas and moisture transport within porous media. It lays a specific theoretical foundation for laser soil remediation technology.

Constructing neural networks with pre-specified dynamics

A main goal in neuroscience is to understand the computations carried out by neural populations that give animals their cognitive skills. Neural network models allow to formulate explicit hypotheses regarding the algorithms instantiated in the dynamics of a neural population, its firing statistics, and the underlying connectivity. Neural networks can be defined by a small set of parameters, carefully chosen to procure specific capabilities, or by a large set of free parameters, fitted with optimization algorithms that minimize a given loss function. In this work we alternatively propose a method to make a detailed adjustment of the network dynamics and firing statistic to better answer questions that link dynamics, structure, and function. Our algorithm—termed generalised Firing-to-Parameter (gFTP)—provides a way to construct binary recurrent neural networks whose dynamics strictly follows a user pre-specified transition graph that details the transitions between population firing states triggered by stimulus presentations. Our main contribution is a procedure that detects when a transition graph is not realisable in terms of a neural network, and makes the necessary modifications in order to obtain a new transition graph that is realisable and preserves all the information encoded in the transitions of the original graph. With a realisable transition graph, gFTP assigns values to the network firing states associated with each node in the graph, and finds the synaptic weight matrices by solving a set of linear separation problems. We test gFTP performance by constructing networks with random dynamics, continuous attractor-like dynamics that encode position in 2-dimensional space, and discrete attractor dynamics. We then show how gFTP can be employed as a tool to explore the link between structure, function, and the algorithms instantiated in the network dynamics.

A modelling study to explore the effects of regional socio-economics on the spreading of epidemics

AbstractEpidemics, apart from affecting the health of populations, can have large impacts on their social and economic behavior and subsequently feed back to and influence the spreading of the disease. This calls for systematic investigation which factors affect significantly and either beneficially or adversely the disease spreading and regional socio-economics. Based on our recently developed hybrid agent-based socio-economy and epidemic spreading model we perform extensive exploration of its six-dimensional parameter space of the socio-economic part of the model, namely, the attitudes towards the spread of the pandemic, health and the economic situation for both, the population and government agents who impose regulations. We search for significant patterns from the resulting simulated data using basic classification tools, such as self-organizing maps and principal component analysis, and we monitor different quantities of the model output, such as infection rates, the propagation speed of the epidemic, economic activity, government regulations, and the compliance of population on government restrictions. Out of these, the ones describing the epidemic spreading were resulting in the most distinctive clustering of the data, and they were selected as the basis of the remaining analysis. We relate the found clusters to three distinct types of disease spreading: wave-like, chaotic, and transitional spreading patterns. The most important value parameter contributing to phase changes and the speed of the epidemic was found to be the compliance of the population agents towards the government regulations. We conclude that in compliant populations, the infection rates are significantly lower and the infection spreading is slower, while the population agents’ health and economical attitudes show a weaker effect.

The relative James construction and its application to homotopy groups

In this paper, we develop the new method to compute the homotopy groups of the mapping cone Cf=Y∪fCX beyond the metastable range by analysing the homotopy of the n-th filtration of the relative James construction J(X,A) for CW-pair A↪iX, defined by B. Gray, which is homotopy equivalent to the homotopy fiber of the pinch map X∪iCA→ΣA. As an application, we compute the 5 and 6-dim unstable homotopy groups of 3-dimensional mod 2r Moore spaces for all positive integers r.

Fermion localization on the brane in Ricci-inverse gravity

This study aims to analyze the effects of modified gravity via anti-curvature tensor on a gravitational model set up within a 5-dimensional space–time, focusing on brane-world scenarios. The anti-curvature tensor introduces innovative configuration that is equal to the inverse of the Ricci tensor. In this analysis, we consider f(R,A)=(R+αA), where the coupling parameter α influences both vacuum regions outside the brane and the core region within it. Through analysis, this study uncovers alterations in fermion localization, particularly impacting left-chirality fermion. To quantify fermion localization, probabilistic metrics such as Shannon entropy and relative probability are employed, demonstrating a heightened level of certainty as α values increase. These findings shed significant light on the dynamics of extra-dimensional models, providing valuable insights into the realms of particle physics and cosmology.

Institutional structure and governance capability in universities: an empirical study from the perspectives of time, space, and quantity dimensions

Institutions are pivotal in university governance, symbolizing stable organizational power reflective of governance capacity. The strategic organization of a university’s internal structures aims to align with its developmental goals. The effectiveness of these arrangements is evaluated by their congruence with the university’s characteristics and norms, aiming to enhance governance for growth and sustainability. Thus, the primary aim of this study is to determine whether this layout can strengthen the university’s governance ability, enhancing its prospects for survival and development. This study introduces a novel theoretical framework across the dimensions of time, space, and quantity, utilizing governance elements to assess the impact of institutional layouts on governance capabilities. Data were gathered through a self-developed survey questionnaire, with a total of 742 valid responses collected, and by employing a high-dimensional fixed-effects model, we found that the three-dimensional institutional layouts significantly impact governance capabilities, with effects varying by the institution’s affiliation. Furthermore, the mechanism analysis shows that university governance capabilities are also manifested through different configurations of governance elements under institutional layout, and are influenced by the responsiveness, collaboration, and expansion of the entire institutional system. Moreover, our analysis indicates a threshold effect in the tenure of institutional members, where both excessive and insufficient enthusiasm impact governance capabilities differently. This suggests the importance of a strategic institutional layout that aligns with the governance elements’ dynamics of timeliness, flexibility, distribution, and scarcity across time, space, and quantity. Achieving an optimal arrangement enhances the university’s governance efficiency significantly. In light of these findings, policy implications were proposed.

An approach to modeling the spatial interaction of point sets on integer regular grids

The paper demonstrates a generalized approach to modeling the interaction of points and point sets on integer regular grids in metric spaces. The modeling process is based on the definition of spatial relations in "Point-Set" and "Set-Set" pairs, which allows to determine the spatial interaction between arbitrary geometric objects, defined as grid-based geometric models (GGM), which represent point sets on regular grids, generalized schemes of spatial interaction are developed in the work. As a result of the work, software was developed for conducting computer experiments on simulation of interaction in metric spaces of arbitrary dimensions and visualization of their results. The developed approach was tested on data sets of different dimensions. Figs.: 10. Refs.: 11 titles.

Zirconia full-arch implant prostheses: Survival, complications, and prosthetic space dimensions with 115 edentulous jaws.

To assess the survival and complication rates of 115 monolithic zirconia implant-supported fixed complete dental prostheses (IFCDPs) with an up to 6-year follow-up. One hundred fifteen edentulous jaws (71 patients) underwent complete-arch implant treatment with a digital workflow and were rehabilitated with monolithic zirconia IFCDPs. The primary outcome was to assess survival and complication rates while the secondary outcome was to measure the cross-sectional dimensions (prosthetic space) of those 115 monolithic zirconia IFCDPs and to correlate potential technical complications with the prosthetic space dimensions. Out of the 115 zirconia IFCDPs, 2 fractured, yielding a 98.6% survival rate up to a 6-year follow-up. The most commom minor technical complications were loss of screw access channel filling and porcelain chipping for the modified monolithic IFCDPs. There was no significant association between the count and type of complications and jaw location (maxilla vs. mandible) or prosthesis type (FP1 vs. FP3), according to Fisher's exact test. For maxillary zirconia IFCDPs, the mean square surface for the at the posterior abutment cross-sectional area was 25.18mm2 at the lingual side of the abutment and 34.19mm2 at the buccal side, respectively. The anterior abutment cross-sectional area was 33.92mm2 at the lingual side of the abutment and 29.49mm2 at the buccal side, respectively. For mandibular zirconia IFCDPs, the mean square surface at the posterior abutment cross-sectional area was 29.89 mm2 at the lingual side of the abutment and 39.05mm2 at the buccal side, respectively. The anterior abutment cross-sectional area was 27.07mm2 at the lingual side of the abutment and 56.50mm2 at the buccal side, respectively. At the connector cross-sectional area, the mean square surface for the maxillary zirconia IFCDPs was 64.33 and 90.56mm2 for the mandibular zirconia IFCDPs. The two fractures occurred in the midline (anterior area) for both maxillary FP1 prosthesis and mandibular FP3 prosthesis. The mean surface area at the connector for the maxillary FP1 prosthesis was 28.50 and 82.11mm2 for the mandibular FP3 prosthesis, and was within the range of IFCDP connector square surface area. There was no significant association between the thickness of the zirconia prosthesis and the encountered prosthesis fractures. Monolithic zirconia IFCDPs yielded a 98.6% survival rate, after a mean observation period of 62 months with an SE of 3.1. The connector mean surface area in the two fractured IFCDPs was within the square surface range (minimum-maximum) as for the remaining 113 complication-free IFCDPs.

High-dimensional maximum-entropy phase space tomography using normalizing flows

Particle accelerators generate charged-particle beams with tailored distributions in six-dimensional position-momentum space (phase space). Knowledge of the phase space distribution enables model-based beam optimization and control. In the absence of direct measurements, the distribution must be tomographically reconstructed from its projections. In this paper, we highlight that such problems can be severely underdetermined and that entropy maximization is the most conservative solution strategy. We leverage —invertible generative models—to extend maximum-entropy tomography to six-dimensional phase space and perform numerical experiments to validate the model's performance. Our numerical experiments demonstrate consistency with exact two-dimensional maximum-entropy solutions and the ability to fit complicated six-dimensional distributions to large measurement sets in reasonable time. Published by the American Physical Society 2024

Multiparty Quantum Key Agreement Based on d$d$‐dimensional Bell States

AbstractIn this paper, on the design process of a multiparty quantum key agreement protocol within a ‐dimensional Hilbert space is elaborated upon. A circular‐type multiparty quantum key agreement protocol based on the generalized Bell state is introduced. To enhance security against external attacks, decoy states into the transmission process is incorporated. Transmission sequences of the generalized Bell state and decoy states are passed between participants. The participants then encode their secret information into the corresponding particles. Ultimately, all participants are able to derive the same key. In addition, a combination of ‐dimensional Pauli operators is utilized, making the proposed protocol feasible with current technology. Analysis and protection against intercept‐resend attack, entangle‐measure attack and dishonest participants attacks, demonstrating the feasibility of the protocol in a ‐dimensional Hilbert space. The protocol has certain advantages over other protocols in terms of a comprehensive consideration of security and efficiency.

Hybrid Resonant Metasurfaces with Configurable Structural Colors

AbstractMetasurfaces are sub‐wavelength nanostructures with the potential to overcome the limitations of traditional optics. Existing dielectric metasurfaces, however, are often limited to geometric primitives, which hamper their application in emergent hybrid metasurfaces. Here, a simple fabrication scheme for non‐primitive metasurfaces that addresses this limitation is introduced. Due to their broken out‐of‐plane symmetry, these nanostructures provide a new dimension in the design space. Taking inspiration from bio‐photonic systems in nature, using these elements complex hybrid metasurfaces are designed that encompass an ordered and a disordered phase. The capabilities of this hybrid optical systems are illustrated by generating configurable structural colors with extra ordinary resolution. Furthermore, the local control of light over a broad bandwidth is demonstrated and a maximum coupling efficiency of more than 97% is achieved.

Holographic phenomenology via overlapping degrees of freedom

Abstract The holographic principle suggests that regions of space contain fewer physical degrees of freedom than would be implied by conventional quantum field theory. Meanwhile, in Hilbert spaces of large dimension $2^n$, it is possible to define $N \gg n$ Pauli algebras that are nearly anti-commuting (but not quite) and which can be thought of as ``overlapping degrees of freedom". We propose to model the phenomenology of holographic theories by allowing field-theory modes to be overlapping, and derive potential observational consequences. In particular, we build a Fermionic quantum field whose effective degrees of freedom approximately obey area scaling and satisfy a cosmic Bekenstein bound, and compare predictions of that model to cosmic neutrino observations. Our implementation of holography implies a finite lifetime of plane waves, which depends on the overall UV cutoff of the theory. To allow for neutrino flux from blazar TXS 0506+056 to be observable, our model needs to have a cutoff $k_{\mathrm{UV}} \lesssim 500\, k_{\mathrm{LHC}}\,$. This is broadly consistent with current bounds on the energy spectrum of cosmic neutrinos from IceCube, but high energy neutrinos are a potential challenge for our model of holography. We motivate our construction via quantum mereology, \ie using the idea that EFT degrees of freedom should emerge from an abstract theory of quantum gravity by finding quasi-classical Hilbert space decompositions. We also discuss how to extend the framework to Bosons. Finally, using results from random matrix theory we derive an analytical understanding of the energy spectrum of our theory.\ \ The numerical tools used in this work are publicly available within the \verb|GPUniverse| package, \url{https://github.com/OliverFHD/GPUniverse}~.

Quantum exploration of high-dimensional canyon landscapes

Canyon landscapes in high dimension can be described as manifolds of small, but extensive dimension, immersed in a higher dimensional ambient space and characterized by a zero potential energy on the manifold. Here we consider the problem of a quantum particle exploring a prototype of a high-dimensional random canyon landscape. We characterize the thermal partitionfunction and show that around the point where the classical phase space has a satisfiability transition so that zero potential energy canyons disappear, moderate quantum fluctuations have a deleterious effect: they induce glassy phasesat temperature where classical thermal fluctuations alone would thermalize the system. Surprisingly we show that even when, classically, diffusion is expected to be unbounded in space, the interplay between quantum fluctuations and the randomness of the canyon landscape conspire to have a confining effect.

Approximation of a two‐dimensional Gross–Pitaevskii equation with a periodic potential in the tight‐binding limit

AbstractThe Gross–Pitaevskii (GP) equation is a model for the description of the dynamics of Bose–Einstein condensates. Here, we consider the GP equation in a two‐dimensional setting with an external periodic potential in the ‐direction and a harmonic oscillator potential in the ‐direction in the so‐called tight‐binding limit. We prove error estimates which show that in this limit the original system can be approximated by a discrete nonlinear Schrödinger equation. The paper is a first attempt to generalize the results from [19] obtained in the one‐dimensional setting to higher space dimensions and more general interaction potentials. Such a generalization is a non‐trivial task due to the oscillations in the external periodic potential which become singular in the tight‐binding limit and cause some irregularity of the solutions which are harder to handle in higher space dimensions. To overcome these difficulties, we work in anisotropic Sobolev spaces. Moreover, additional non‐resonance conditions have to be satisfied in the two‐dimensional case.